Is this a good Facebook ads strategy to sell my eBook?

I am new to internet marketing, I am going to promote my eBook using Facebook ads. Is this a good strategy?:

1. Get the Facebook campaign to send users to my one page landing page
2. Ask users to enter their email to receieve a smaller free ebook that is still useful for them
3. Use the email list that i've built to market my paid eBook.

Is this an effective strategy? If so, how should I structure the emails to encourage eBook sales? What website / software should I use as my eBook purchase page?

There are several software that can be used to sell ebooks like paddle, jvzoo and could be more. And yes you could use Facebook ads to prepare an email list that you can use later on to sell your ebook.
Start with information and free things to see what kind of open rate are you achieving and after that start pushing your sales copy.

I think your strategy should be based around your niche and what they want. Where are the people that would read your book hanging out? There maybe forums about your book topic etc... what is your book about (what niche)

That is a good strategy to build your email list to promote the ebook also to sell other products in the future. So look at it as a long term strategy also.

When you send out emails to your email list you can put quotes from the book or samples of a few pages so others can see what it's about. Don't promote the book in every email, maybe 1 out of every 3 emails. This way you won't look like you are only trying to sell the ebook.